Any number raised to the power of 1 is that number One as Exponent Any number raised to the power of 1 is that number x1 = x 61 = 6

Any non-zero number raised to the power of 0 is equal to 1. Zero as Exponent Any non-zero number raised to the power of 0 is equal to 1. x0 = 1 70 = 1

Negative One as Exponent Write the base as its reciprocal x-1 = 1/x 4-1 = 1/4

Multiplication of Powers Powers of the same base may be multiplied by adding their exponents. xmxn = xm+n x2x3 = x2+3 = x5

Powers of the same base may be divided by subtracting their exponents. Division of Powers Powers of the same base may be divided by subtracting their exponents.

Powers of Powers Powers of the same base may be raised to another power by multiplying their exponents. (xm)n = xmn (x2)3 = x2×3 = x6

Apply the exponent to every term inside the parentheses Product to a Power Apply the exponent to every term inside the parentheses (xy)n = xnyn (2y)3 = 23y3 =8y3

Dividing different bases with the same exponent The exponent gets applied to both parts of the fraction – numerator & denominator = 16 𝑦 2

𝑥 −3 = 1 𝑥 3 Negative Exponents The base gets written as the reciprocal and the power becomes positive on the denominator x-n = 1/xn 𝑥 −3 = 1 𝑥 3

Different Bases raised to the same power Multiply the bases together and raise the product to that power (x)n(y)n = (xy)n (4)3(t)3 = (4t)3

Commutative Property of Addition As long as the numbers are all being added together, you can change the order of your numbers. a+b+c = a+c+b 6+3+4 = 6+4+3 9+4 = 10+3 13 = 13

Associative Property of Addition As long as the numbers are all being added together, you move the parentheses to regroup the numbers. (a+b)+c = a+(b+c) (7+2)+8 = 7+(2+8) (9)+8 = 7+(10) 17 = 17

Property of Multiplication Associative Property of Multiplication As long as the numbers are all being multiplied together, you move the parentheses to regroup the numbers. (a·b)·c = a·(b·c) (5·9)·2 = 5·(9·2) (45)·2 = 5·(18) 90 = 90

Property of Multiplication Commutative Property of Multiplication As long as the numbers are all being multiplied together, you can change the order of your numbers. a·b·c = a·c·b 2·7·5 = 2·5·7 14·5 = 10·7 70 = 70

Distributive Property The Distributive Property lets you multiply a sum by multiplying each addend separately and then add the products. a(b+c) = ab+ac 13(2+8) = 13·2+13·8